Homework_3_Solutions

Homework_3_Solutions - Assignment 3 Solutions 1 a) The...

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Assignment 3 Solutions 1 a) The following are the plots of the time series, ACF and PACF (of all the given data): Figure : Scatter Plot for Whole Dataset Figure : ACF and PACF Plots of Whole Dataset One can see from the time series above that the data are not stationary. Rather, there seems to be an increasing trend over time. The slow decay (non-exponential nature) of the ACF plot and the spikes in the PACF plot indicate high autocorrelation between the lags of the time series (from both the MA and AR components respectively). Thus, time series modelling is required in order to account for these factors. b) By taking the natural logarithm of the data and differencing each datum with its previous lag (except for the first point) on the training dataset , the time series is detrended. This can be seen in the following figure:
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Figure : Plot of Detrended Time Series Data The transformed data seem to both centre around zero and have constant variation. A suitable test for stationarity would the Augmented Dickey-Fuller test where the null hypothesis assumes that a unit root is present (i.e. the time series is non-stationary) as opposed to the alternate hypothesis that a unit root is not present. The following is the R-Code. > library(tseries) > adf.test(diff(log(tr_ISOL_RATE))) Augmented Dickey-Fuller Test data: diff(log(tr_ISOL_RATE)) Dickey-Fuller = -7.3221, Lag order = 6, p-value = 0.01 alternative hypothesis: stationary Warning message: In adf.test(diff(log(tr_ISOL_RATE))) : p-value smaller than printed p-value Thus, with a p-value smaller than 0.05, the null hypothesis is rejected and one concludes that the transformed time series is stationary. c) The model used here was a SARIMA on the logarithmic values of the training dataset .
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This note was uploaded on 02/23/2012 for the course STAT 443 taught by Professor Yuliagel during the Spring '09 term at Waterloo.

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Homework_3_Solutions - Assignment 3 Solutions 1 a) The...

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